The techniques are explained without reliance on equations and algebra so that new users will understand when to use these approaches and how they are really just special applications of ordinary regression. Using real data from the Programme for International Student Assessment and the British Household Panel Study the authors shows how to model random intercept models and random coefficient models in a way that makes sense and can be retained and repeated.
Chapter 1: What Is Multilevel Modeling and Why Should I Use It? Mixing levels of analysis Theoretical reasons for multilevel modeling What are the advantages of using multilevel models? Statistical reasons for multilevel modeling Assumptions of OLS Software How this book is organized Chapter 2: Random Intercept Models: When intercepts vary A review of single-level regression Nesting structures in our data Getting starting with random intercept models What do our findings mean so far? Changing the grouping to schools Adding Level 1 explanatory variables Adding Level 2 explanatory variables Group mean centring Interactions Model fit What about R-squared? R-squared? A further assumption and a short note on random and fixed effects Chapter 3: Random Coefficient Models: When intercepts and coefficients vary Getting started with random coefficient models Trying a different random coefficient Shrinkage Fanning in and fanning out Examining the variances A dichotomous variable as a random coefficient More than one random coefficient A note on parsimony and fitting a model with multiple random coefficients A model with one random and one fixed coefficient Adding Level 2 variables Residual diagnostics First steps in model-building Some tasters of further extensions to our basic models Where to next? Chapter 4: Communicating Results to a Wider Audience Creating journal-formatted tables The fixed part of the model The importance of the null model Centring variables Stata commands to make table-making easier What do you talk about? Models with random coefficients What about graphs? Cross-level interactions Parting words
